To compare the medians of two data sets, you first need to calculate each median and then directly compare the resulting values.

To determine the median of a data set, start by arranging the numbers in ascending order. If the data set contains an odd number of values, the median is the middle number. For instance, in the data set $\{3, 5, 7\}$, the median is $5$. Conversely, if the data set has an even number of values, the median is calculated as the average of the two middle numbers. For example, in the data set $\{2, 4, 6, 8\}$, the median is computed as follows:

Once you have obtained the medians for both data sets, you can compare them directly. If one median is greater than the other, it indicates that the central value of that data set is higher. For example, if the median of data set A is $10$ and the median of data set B is $15$, this shows that data set B has a higher central value.

Comparing medians is particularly useful because the median is resistant to the influence of extreme values, known as outliers. This property makes it a reliable measure of central tendency, especially when dealing with skewed distributions. For instance, consider the data set $\{1, 2, 3, 100\}$. The median of this set is $2.5$, which more accurately reflects the central tendency than the mean would, as the mean is significantly affected by the outlier $100$.

In summary, by calculating and comparing the medians of two data sets, you can gain valuable insights into their central tendencies.